Supersymmetry with R-Parity Breaking Contact Interactions and Resonance Formation in Lepton

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DYNAMICAL BREAKING OF SUPERSYMMETRY

Received 29 Aห้องสมุดไป่ตู้ril 1981
General conditions for dynamical supersymmetry breaking are discussed. Very small effects that would usually be ignored, such as instantons of a grand unified theory, might break supersymmetry at a low energy scale. Examples are given (in 0 + I and 2 + 1 dimensions) in which dynamical supersymmetry breaking occurs. Difficulties that confront such a program in four dimensions are described.
I. Introduction Supersymmetry has fascinated particle physicists since it was first discovered [1]. It is an outstanding example of a known mathematical structure which may plausibly be absorbed in the future into our understanding of particle physics. Of course, if nature really is described by a supersymmetric theory, the symmetry must be spontaneously broken [2]. At what energies does the symmetry breaking occur? It might very well occur at energies of order the Planck mass. In that case supersymmetry would be relevant to particle physics at "ordinary" energies only indirectly, in as much as the broken supersymmetry might make predictions concerning particle quantum numbers and relations among masses and coupling constants. On the other hand, it is possible that supersymmetry breaking occurs at "ordinary" energies like a few hundred GeV or a few TeV. In this case, ordinary particle physics, at energies much less than the Planck mass, is presumably described by a renormalizable, globally supersymmetric model. There has been some success [3] in constructing realistic models of this sort for ordinary particle interactions. If supersymmetry breaking does occur at ordinary particle physics energies, we must ask why the energy scale of supersymmetry breaking is so tiny compared to the natural energy scale of gravity and supergravity [4], which is presumably the Planck mass. This is a variant of the "hierarchy problem" [5]: why is the mass scale of ordinary particle physics so much less than the mass scale of grand unification or gravitation?

Supersymmetric Grand Unification Model with the Orbifold Symmetry Breaking in the Six Dimen

a r X i v :h e p -p h /0108152v 1 19 A u g 2001UT-962Supersymmetric Grand Uniﬁcation Model with the Orbifold Symmetry Breaking in the Six Dimensional Supergravity T.Watari a and T.Yanagida a,b a Department of Physics,University of Tokyo,Tokyo 113-0033,Japan b Research Center for the Early Universe,University of Tokyo,Tokyo 113-0033,Japan Abstract We construct supersymmetric (SUSY)grand uniﬁcation (GUT)models in the six dimensional space-time where the GUT symmetry is broken down to the standard-model gauge group by a simple orbifolding T 2/Z 4or T 2/Z 6and a pair of massless Higgs doublets in the SUSY standard model are naturally obtained.Since the background geometry here is simple compared with models using the Scherk-Schwarz mechanism,one might hope for an approximate gauge coupling uniﬁcation in the present models.Here,the presence of the massless Higgs multiplets in the bulk is quite natural,since the anomaly cancellation inthe six dimensional space-time requires N=2hyper multiplets in the bulk,some of which are origins of the Higgs doublets.However,the origin of the quarks and leptons is still not clear at all.Search for a solution to the doublet-triplet splitting problem in the supersymmetric (SUSY)grand uniﬁcation theory(GUT)has led us to consider various extensions of the minimal SU(5)SUSY-GUT[1,2,3].Recently,Kawamura[4]has pointed out an interesting solution to this problem utilizing an S1/Z2orbifold in aﬁve dimensional space-time,which is deeply related to the early suggestion by Witten[5]1.Although this original model is non SUSY-GUT,it is easily extended to the SUSY-GUT if one assumes an S1/(Z2 σ1 ×Z′2 σ2 )orbifold[7,8].Here,this orbifold is also regarded as R1/(Z σ1σ2 ×′Z2 σ1 ),where the Z σ1σ2 gives the symmetry-breaking boundary condition a la Scherk-Schwarz[9].A number of interesting features in this approach have been discussed[10].However,it is claimed[11]recently that the Scherk-Schwarz breaking is equivalent to the Wilson line breaking[12]localized at aﬁxed point.Thus, the nontrivial background of gaugeﬁeld exists at theﬁxed point,and its eﬀect to the tree level gauge coupling is incalculable and it may be beyond the naive dimensional analysis[8]2.Therefore,it is not necessarily obvious to maintain the gauge coupling uniﬁcation even at the tree level.The purpose of this letter is to show that a SUSY-GUT model with the orbifold GUT breaking mechanism is constructed in the six dimensional space-time without the Scherk-Schwarz breaking3.In this letter,we use the term“orbifold GUT breaking model”as a class of models that do not use the Scherk-Schwarz(or boundary breaking) mechanism.Since the background geometry here is simple compared with models using the Scherk-Schwarz mechanism,one might hope for an approximate gauge coupling uniﬁcation in the present models.We consider a simple orbifold T2/Z4.Weﬁnd that only a pair of the Higgs doublets H f and¯H f survive together with the gauge multiplets of SU(3)C×SU(2)L×U(1)Y in the extra two dimensional bulk.The matter multiplets 5∗and10are assumed to reside on aﬁxed point that preserves SU(5)symmetry.Wealsoﬁnd that a similar model can be constructed on another simple orbifold T2/Z6.Weﬁrst note that theﬁve dimensional space-time is too small to have the desired orbifold GUT breaking model(without the Scherk-Schwarz mechanism).The orbifold projection associated with the S1/Z2compactiﬁcation is not enough to eliminate all the unwanted particles contained in the N=2SUSY SU(5)multiplets.Such an elimination is possible only by using the Scherk-Schwarz mechanism in the S1/(Z2×Z′2)≃R1/(Z×′Z2)compactiﬁcation.Therefore,we consider the orbifold GUT breaking model in the six dimensional space-time.Furthermore,there is another reason to assume the higher dimensional space-time;the R-symmetry that is a crucial and unique symmetry to forbid a constant term in the superpotential[15]may arise from a rotation symmetry in the extra space.In this sense the present analysis provides theﬁrst basic and natural GUT model in a higher dimensional space-time4.We restrict ourselves to the six dimensional supergravity in this letter,since if we go further the consistency condition becomes more restrictive.We do not consider that the eﬀectiveﬁeld theory should be necessarily formulated in the ten dimensional supergravity,even if the underlying fundamental theory is given by the string theory.The possible rotational symmetry that the two dimensional torus T2in the extra dimensional space possesses is Z2,Z3,Z4or Z6.These are the symmetries that rotate the4th-5th plane byπ,2π/3,π/2andπ/3,respectively.We require that the orbifold projection condition explicitly distinguishes the color SU(3)and theﬂavor SU(2)of the SU(5)indices and breaks the SU(5)GUT down to the standard-model gauge group.The N=2SU(5)vector multiplet propagates in the six dimensional bulk.The lengths L of the extra dimensions are assumed to be of order of1/(GUT scale)and the fun-damental scale of the theory M∗is of order1017GeV.This lower cut-oﬀscale is a crucial point in keeping the approximate gauge coupling uniﬁcation at the eﬀective GUT scale∼1016GeV[8,16].The volume of the extra two dimensional space5is about (M∗L)2∼102.Now that the SU(5)vector multiplet propagates in the six dimensional bulk,the six dimensional box anomaly must be canceled.Six dimensional box anomalies consist ofpure gauge anomalies tr(F4)and(tr(F2))2,a gauge-gravity mixed anomaly tr(F2)tr(R2) and pure gravitational anomalies[18].Among these,pure gravitational anomalies can be canceled by introduction of SU(5)singletﬁelds and reducible anomalies(tr(F2))2 and tr(F2)tr(R2)can be canceled by the Green-Schwarz mechanism[19].Thus we only care about the pure gauge tr(F4)anomaly of the SU(5)gauge theory.In(1,0)-SUSY (N=2SUSY in four dimensional sense)gauge theories in six dimensions,N=2hyper multiplets have chirality opposite to that of the N=2vector multiplet.Therefore,the pure gauge box anomaly from the gauge fermions of the N=2SU(5)vector multiplet can be canceled by introducing N=2hyper multiplets.The anomaly of the SU(n)N=2 vector multiplet is−2n times that of the N=2hyper multiplet in SU(n)-fundamental representation(up to reducible anomaly)[18],and hence we introduce ten(5+5∗)hyper multiplets in the six dimensional bulk6.We expect that the four dimensional N=1vector multiplets of the SU(3)C×SU(2)L×U(1)Y in the minimal SUSY standard model(MSSM)comes from the above N=2SU(5) vector multiplet.Since we introduced N=2hyper multiplets in5+5∗representation,it is possible that the H f and¯H f N=1chiral multiplets in the MSSM also originate from the bulkﬁelds.Spectrum of massless particles that live in the bulk are determined by the orbifold projection condition that distinguishes the color SU(3)and theﬂavor SU(2),and hence the remaining particles may be chosen as only doublets by adopting an appropriate orbifold projection as shown below.The phenomenological reason for which we identify the Higgs as bulkﬁelds(not asﬁxed pointﬁelds),will be explained later.On the contrary,we postulate by hand that the quarks and leptons N=1chiral multiplets,(5∗+10),reside on orbifoldﬁxed points.This is the weakest point in the present approach.In the model construction of the orbifold GUT breaking,the existence of theﬁxed point that preserves the SU(5)symmetry is an important ingredient[8].A natural explanation of the anomaly cancellation in terms of the SU(5)GUT which is nothing but a miracle in the standard model,the charge quantization of the U(1)Y,and the bottom-tau Yukawa uniﬁcation are the major reasons that we believe SUSY-GUT alongwith the gauge coupling uniﬁcation suggested from the experiments.The above three features are still maintained if the orbifold geometry has aﬁxed point that preserves the four dimensional SU(5)GUT symmetry even though the orbifold GUT breaking model has no complete higher dimensional SU(5)symmetry.We consider the model in which the three families of quarks and leptons5∗+10reside on such aﬁxed point.In order to have aﬁxed point which preserves the SU(5)symmetry,the orbifold group must have nontrivial and proper subgroup.First,the isotropy group associated to such aﬁxed point7is not trivial by deﬁnition.Secondly,if the isotropy group were identical to the whole orbifold group,then the orbifold projection associated to the isotropy group of such aﬁxed point would distinguish the color SU(3)and theﬂavor SU(2)subgroups of the SU(5),and hence the SU(5)symmetry would not be preserved. Therefore,the isotropy group of such aﬁxed point is nontrivial and proper subgroup of the whole orbifold group.This means that the orbifold group candidate are Z4and Z6since Z2and Z3do not have such a subgroup.Therefore,we consider the T2/Z4 σ and T2/Z6 σ model where theσis the generator of the each orbifold group Z4and Z6.Let usﬁrst consider the model on T2/Z4 σ orbifold.The generatorσof the Z4 transformation rotates the4th-5th plane byπ/2:(z≡(x4+ix5))→σ·z=e i(θ=2π7Isotropy(sub)group of a point is a subgroup of a transformation group,say the orbifold group, which consists of elements thatﬁx the point.8In this letter,we call theﬁxed point whose isotropy group is Z2 σ2 as Z2 σ2 ﬁxed point for brevity.Similar terminology is also used later in the T2/Z6orbifold model.F(x,z)j=e iθn j γσF(x,e iθz)j,¯F(x,z)j=e iθ(−1−n j) γ−1σ¯F(x,e iθz)j,(3) whereθ=(2π)/4.Rotational charges n j for the hyper multiplet can be n/2(n= 0,1,2,3,...). γσis the(5×5)gauge twisting matrix associated to the generatorσthat must satisfy( γσ)4=1.We take the gauge twisting matrix γσasγσ=diag(e iθm,e iθm,e iθm,e i(θm+π),e i(θm+π)),(4) where m is an arbitrary integer andθ=(2π)/4.Under this choice,the Z2 σ2 ﬁxed point preserves the SU(5)symmetry because the gauge twisting matrix γσ2≡( γσ)2∝1 does not make any discrimination between the color SU(3)and theﬂavor SU(2).We put the three families of quarks and leptons on thisﬁxed point.Now we can see that the massless particles(Kaluza-Klein zero modes)from the N=2 SU(5)vector multiplet are just the N=1vector multiplets of the MSSM.Only one pair of the N=1chiral multiplets H f from the F1and the¯H f from the¯F2survive the orbifold projection conditions Eq.(3)if we take n1=(2−m),n2=(1−m)and n j(j=3, (10)to be half integers.These are exactly the pair of Higgs doublets in the MSSM.No other unwanted particle remains massless.We can also see that the triangle anomalies which might appear atﬁxed points because of the orbifolding completely vanish[20].We obtain the desired massless Higgs multiplets H f and¯H f in the bulk.As a matter of fact,this is a necessary property as long as the third family of the quarks and leptons reside on the SU(5)preservingﬁxed point.The reason is the following.Suppose that the two Higgs doublets reside on one of the two Z4 σ ﬁxed points and the third family reside on the Z2 σ2 ﬁxed point.Let us consider how the Yukawa couplings in the superpotential are generated.Since the quark and lepton multiplets are separated from the two Higgs doublets by the distance M∗L∼10,an exchange of particles of mass of order of the fundamental scale M∗is not enough to induce the Yukawa couplings because of the damping of the wave function e−M∗L<∼10−4.Only the Kaluza-Klein particles of the5+5∗hyper multiplets can do the job.However,we can see that all those Kaluza-Klein particles have zero wave function at the Z4ﬁxed points in models where no massless Higgs multiplet remains in the bulk.Therefore,necessary Yukawa couplings are not generated by the exchanges of the Kaluza-Klein particles.It is easy to see that a similar argument to the above also holds in the model ofT2/Z6 σ orbifold.The generatorσrotates the4th-5th plane byπ/3:z→e iθz θ=2πported by“Priority Area:Supersymmetry and Uniﬁed Theory of Elementary Particles (#707)”(T.Y.).References[1]A.Masiero,D.V.Nanopoulos,K.Tamvakis and T.Yanagida,Phys.Lett.B115(1982)380;I.Antoniadis,J.Ellis,J.S.Hagelin and D.V.Nanopoulos,Phys.Lett.B194(1987)231.[2]S.Dimopoulos and F.Wilczek,NSF-ITP-82-07;M.Srednicki,Nucl.Phys.B202(1982)327.[3]T.Yanagida,Phys.Lett.B344(1995)211[hep-ph/9409329];J.Hisano and T.Yanagida,Mod.Phys.Lett.A10(1995)3097[hep-ph/9510277];T.Hotta,K.I.Izawa and T.Yanagida,Phys.Rev.D53(1996)3913[hep-ph/9509201],Phys.Rev.D54(1996)6970[hep-ph/9602439];K.I.Izawa and T.Yanagida,Prog.Theor.Phys.97(1997)913[hep-ph/9703350].[4]Y.Kawamura,Prog.Theor.Phys.103(2000)613[hep-ph/9902423].[5]P.Candelas,G.T.Horowitz,A.Strominger and E.Witten,Nucl.Phys.B258(1985)46;E.Witten,Nucl.Phys.B258(1985)75.[6]Y.Imamura,T.Watari and T.Yanagida,hep-ph/0103251;T.Watari and T.Yanagida,hep-ph/0108057;C.Csaki,G.D.Kribs and J.Terning,hep-ph/0107266.[7]Y.Kawamura,Prog.Theor.Phys.105(2001)999[hep-ph/0012125].[8]L.Hall and Y.Nomura,Phys.Rev.D64(2001)055003[hep-ph/0103125].[9]J.Scherk and J.H.Schwarz,Nucl.Phys.B153(1979)61;J.Scherk and J.H.Schwarz,Phys.Lett.B82(1979)60.[10]G.Altarelli and F.Feruglio,Phys.Lett.B511(2001)257[hep-ph/0102301];T.Kawamoto and Y.Kawamura,hep-ph/0106163;A.Hebecker and J.March-Russell,hep-ph/0106166;N.Haba,T.Kondo,Y.Shimizu,T.Suzuki and ai,hep-ph/0108003.[11]A.Hebecker and J.March-Russell,hep-ph/0107039.See also,L.J.Hall,H.Murayama and Y.Nomura,hep-th/0107245.[12]Y.Hosotani,Phys.Lett.B126(1983)309,Annals Phys.190(1989)233.[13]J.Polchinski,String Theory,(Cambridge University Press,UK,1998).[14]T.Asaka,W.Buchmuller and L.Covi,hep-ph/0108021;L.Hall,Y.Nomura,T.Okui and D.Smith,hep-ph/0108071.[15]K.I.Izawa and T.Yanagida,Prog.Theor.Phys.97(1997)913[hep-ph/9703350].[16]R.Contino,L.Pilo,R.Rattazzi and E.Trincherini,hep-ph/0108102.[17]D.E.Kaplan,G.D.Kribs and M.Schmaltz,Phys.Rev.D62(2000)035010[hep-ph/9911293];Z.Chacko,M.A.Luty,A.E.Nelson and E.Ponton,JHEP0001(2000)003[hep-ph/9911323].See also for the early work,K.Inoue,M.Kawasaki,M.Yamaguchi and T.Yanagida, Phys.Rev.D45(1992)328.[18]See,for example,N.Borghini,Y.Gouverneur and M.H.Tytgat,hep-ph/0108094,and references therein.[19]M.B.Green and J.H.Schwarz,Phys.Lett.B149(1984)117.[20]N.Arkani-Hamed,A.G.Cohen and H.Georgi,hep-th/0103135.Figure1:T2/Z4orbifold geometry is described.There are two Z4 σ ﬁxed points(•’s in theﬁgure)and oneﬁxed point(◦in theﬁgure)whose isotropy group is Z2 σ2 .The arrow denotes the identiﬁcation between mirror images under Z4/Z2.This Z2 σ2 ﬁxed point is the SU(5)preservingﬁxed point.Figure2:Geometry of T2/Z6is described.This orbifold has threeﬁxed points whose isotropy groups are all diﬀerent:namely the•(Z3 σ2 ﬁxed),the◦(Z2 σ3 ﬁxed)and the•-◦(Z6 σ ﬁxed)in thisﬁgure.Each of theﬁxed point•and◦can be an SU(5) preservingﬁxed point.Arrows denote the identiﬁcation between mirror images under Z6/Z3(•’s)and Z6/Z2(◦’s),respectively.。

Bottom-up Approach in Supersymmetric Models

1
1
The bottom–up mapping is presented in section 2. Section 3 containes some general results obtained with this method and its application to the low energy region with light chargino and stop. More detailed presentation of the bottom–up mapping and more results can be found in reference [3].
In the small or moderate tan β regime, the dependence of the RG running of these parameters on slepton (and the two ﬁrst generation sfermion) masses comes only through the small hypercharge D-term contributions which we neglect here. Their contribution can be found in [3].
Abstract We present a bottom-up approach to the question of supersymmetry breaking in the MSSM. Starting with the experimentally measurable low energy supersymmetry breaking parameters which can take any values consistent with present experimental constraints, we evolve them up to an arbitrary high energy scale. Approximate analytical expressions for such an evolution, valid for low and moderate values of tan β , are presented. We then discuss qualitative properties of the high energy parameter space and in particular, identify the conditions on the low energy spectrum which are necessary for the parameters at high energy scale to satisfy simple regular pattern such as universality or partial universality. Talk given at the 28th International Conference on High Energy Physics, Warsaw, Poland, July 1996 † On leave of absence from the Institute of Theoretical Physics, Warsaw University, Warsaw, Poland

Signals of Doubly-Charged Higgsinos at the CERN Large Hadron Collider

DESY-08-060, IZTECH-P-08-03, CUMQ-HEP-149, HIP-2008-15/TH
Signals of Doubly-Charged Higgsinos at the CERN Large Hadron Collider
Durmu¸ s A. Demir1,2 , Mariana Frank3 , Katri Huitu4 , Santosh Kumar Rai4 , and Ismail Turan3
Department of Physics, Izmir Institute of Technology, IZTECH, TR35430 Izmir, Turkey. 2 Deutsches Elektronen - Synchrotron, DESY, D-22603 Hamburg, Germany. 3 Department of Physics, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec, CANADA H4B 1R6. and 4 Department of Physics, University of Helsinki and Helsinki Institute of Physics, P.O. Box 64, FIN-00014 University of Helsinki, Finland. Several supersymmetric models with extended gauge structures, motivated by either grand uniﬁcation or by neutrino mass generation, predict light doubly-charged Higgsinos. In this work we study productions and decays of doubly-charged Higgsinos present in left-right supersymmetric models, and show that they invariably lead to novel collider signals not found in the minimal supersymmetric model (MSSM) or in any of its extensions motivated by the µ problem or even in extra dimensional theories. We investigate their distinctive signatures at the Large Hadron Collider (LHC) in both pair– and single–production modes, and show that they are powerful tools in determining the underlying model via the measurements at the LHC experiments.

Phenomenology of low-scale supersymmetry breaking models

IPPP/03/40 DCPT/03/92
Phenomenology of low-scale supersymmetry breaking models
arXiv:hep-ph/0308196v1 19 Aug 2003
Ignacio Navarro∗
IPPP, University of Durham, DH1 3LE Durham, UK.
1
involved, we have no real information available about what these scales are, and for all that we know they could be of order T eV . In this letter, following [3], we will review the (quite distinctive) phenomenological
properties of theories in which all these scales are of order T eV , so the hard SUSY
terms play a relevant role in the phenomenology. Notice that these terms, although do generate quadratic divergencies in the renormalization of scalar masses, do not destabilize any hierarchy since they are suppressed by powers of the mass scale M , that is to
2 for the scalars are typically of order λh ∼ m2 s /M [2,3]. These hard breaking terms are

Parton-Shower Simulations of R-parity Violating Supersymmetric Models

a r X i v :h e p -p h /9912407v 3 3 F eb 2000OUTP-99-26PRAL-TR-1999-080hep-ph/9912407Parton-Shower Simulations of R-parity Violating Supersymmetric Models H.Dreiner ∗1,P.Richardson †2,and M.H.Seymour ∗3∗Rutherford Appleton Laboratory,Chilton,Didcot OX110QX,U.K.†Department of Physics,Theoretical Physics,University of Oxford 1Keble Road,Oxford OX13NP,United Kingdom Abstract We study the colour connection structure of R-parity violating decays and pro-duction cross sections,and construct a Monte Carlo simulation of these processes including colour coherence eﬀects.We then present some results from the imple-mentation of these processes in the HERWIG Monte Carlo event generator.We include the matrix elements for the two-body sfermion and three-body gaugino and gluino decays as well as the two-to-two resonant hard production processes in hadron-hadron collisions.1IntroductionIn the past few years there has been a large amount of interest in R-parity violating(R p) supersymmetric(SUSY)models,motivated by the possible explanations of various exper-imental discrepancies,e.g.[1–9].It has become clear that if we are to explore all possible channels for the discovery of supersymmetry then R p models must be investigated.For a recent review on R-parity violation see[10].In the Minimal Supersymmetric Standard Model(MSSM)a discrete multiplicative symmetry,R-parity(R p)is imposed,R p=(−1)3B+L+2S,(1) where B is the baryon number,L the lepton number and S the spin of the particle.All the Standard Model particles have R p=+1and their super-partners have R p=−1.The conservation of R-parity forbids the terms in the superpotential which violate baryon or lepton number1W R p=1E k+λ′ijkεab L i a Q j b2λ′′ijkεc1c2c3D j c2E i(U i)are the electron(down and up quark)SU(2)singlet superﬁelds, and H n,n=1,2,are the Higgs superﬁelds.We shall neglect the last term in Eqn.2 which mixes the lepton and Higgs SU(2)doublet superﬁelds.For a recent summary of the bounds on the couplings in Eqn.2see[11].This superpotential gives interactions which violate either lepton or baryon number. For example theﬁrst term will give interactions of a slepton and two leptons which violates lepton number.The third term gives an interaction of two quarks and squark, which violates baryon number.When combined with the MSSM superpotential there are also terms involving the interactions of three sleptons/squarks and a Higgs which violate either lepton or baryon number.R p is imposed in the MSSM to avoid the simultaneous presence of the second two terms in Eqn.2.These lead to fast proton decay,in disagreement with the experimental lower bounds on the proton lifetime.However in order to guarantee proton stability it is suﬃcient to forbid only one set of these terms.This is achieved for example by lepton parity(L i,¯E i)→−(L i,¯E i),(3) (Q i,¯U i,¯D i,H1,H2)→(Q i,¯U i,¯D i,H1,H2),(4)which allows the third term in Eqn.2but forbids the remaining terms.Thus baryon number is violated(B)but lepton number is conserved and the proton is stable.Similarly there are symmetries such that lepton number is violated and baryon number is conserved.This also prevents proton decay.Both cases lead to very diﬀerent phenomenology from the MSSM.In the MSSM the conservation of R p implies that1.Sparticles are produced in pairs.2.The lightest supersymmetric particle(LSP)is stable.3.Cosmological bounds on electric-or colour-charged stable relics imply that a stableLSP must be a neutral colour singlet[12].However,in the case of R p models we can have1.Single sparticle production.2.The LSP can decay.As the LSP is unstable it does not have to be a neutral coloursinglet.It can be any supersymmetric particle.3.Lepton or baryon number is violated.In the MSSM,as the LSP is stable,the experimental signatures of SUSY processes typically involve missing transverse energy in collider experiments.However,if R-parity is violated,and the LSP decays in the detector,the missing energy signatures of the MSSM no longer apply or are severely diluted.It therefore requires a diﬀerent experimental search strategy.In particular,in the B case,where theﬁnal state is predominantly hadronic,it may be hard to extract a signal over the QCD background in hadron colliders.Despite the interest in R p and the potential experimental problems,there have been few experimental studies at hadron colliders.Theﬁrst systematic study of R p signatures at hadron colliders was presented in[13].More recent overviews of the search potential at the LHC and Run II of the Tevatron have been presented in[14,15].These studies have been limited by the fact that few simulations have been available.In hadron-hadron collisions the only available Monte Carlo event generator is ISAJET[16]where the R p decays can be implemented using the FORCE command,i.e.the decay mode of a given particle,e.g.the LSP,can be speciﬁed by hand.However there has been no simulation which includes all the decay modes and the single sparticle production processes.Here we present the calculations required to produce a Monte Carlo event generator for the two-body sfermion and three-body gaugino and gluino R p decay modes as well as all two-to-two R p resonant production processes in hadron-hadron collisions.We have only included those production processes where a resonance is possible,so for example processes which can only occur via a t-channel diagram are not included.However where a process can occur via a resonance all the diagrams including non-resonant s-channel and t-channel diagrams have been included.We also discuss colour coherence eﬀects via the angular ordering procedure(which we describe in detail below),and some preliminary results from the implementation of these processes in the HERWIG Monte Carlo event generator[17]. Details of the implementation of supersymmetric processes with and without R p can be found in[18].After a general discussion of the angular ordering procedure in the Standard Model in Section2we discuss the extension to the R p decays and hard production processes inSection3.In Section4we describe the hadronization procedure which we adopt for the R p processes.We then present some preliminary results of the Monte Carlo simulation in Section5.We have made new calculations of all the necessary matrix elements,and include them as an appendix.2Monte Carlo SimulationsIn general a Monte Carlo event generator,for a process involving at least one hadron, consists of three parts.1.A hard scattering process,either of the incoming fundamental particles in leptoncollisions or of a parton extracted from a hadron in hadron initiated processes.2.A parton-shower phase where the partons coming into or leaving the hard processare evolved according to perturbative QCD.3.A hadronization model in which the partons left at the end of the parton-showerphase are formed into the hadrons which are observed.For processes with hadrons in the initial state after the removal of the partons in the hard process we are left witha hadron remnant.This remnant is also formed into hadrons by the hadronizationmodel.We now discuss these three stages in turn.2.1Hard ScatteringThe hard scattering process is described by a matrix element calculated to aﬁxed order in perturbation theory,usually only leading order.The momenta of the particles involved in the collision can then be generated according to the matrix element.The Monte Carlo event generator then needs to take the results of this perturbative calculation,at a high scale,and generate the hadrons which are observed.2.2Parton ShowerIn a scattering process the incoming or outgoing partons can emit QCD radiation,e.g. q→gq and g→gg,or split into quark-antiquark pairs,g→q¯q.A full perturbative treatment of this part of an event is not possible.(If it were possible it would be included in the hard scattering matrix element.)We must therefore make an approximation and focus on the dominant contributions in the showering process.The emission of QCD radiation is enhanced for(a)Collinear Emission and for(b)Soft Emission.We discuss these two below in more detail.Our approximation will consist in focusing on these enhanced regions of radiation.We then discuss this in an explicit example.(a)Collinear EmissionIf we consider the emission of QCD radiation in the collinear limit then,after az-imuthal averaging,the cross section obeys a factorization theorem[19].This canbe understood as follows,the cross section for a process in which one parton pair is much more collinear than any other pair can be written as the convolution of a universal,i.e.process independent,splitting function and the cross section for the same process where the collinear pair is replaced by a single parton of the corre-spondingﬂavour.Due to this functional form we can then apply this procedure to the next most collinear pair in theﬁnal state,and so on.We thus have an iterative rule which leads to a description of multi-partonﬁnal states as a Markov chain[19].This can be viewed as an evolution in some energy-like scale,such as the virtuality, where a parton at high scale is evolved by successive branchings to a lower scale.However,the collinear factorization does not specify what the evolution variable should be,i.e.it has the same form for any variable proportional to the virtuality,e.g.the transverse momentum.This iterative procedure then correctly resums theleading collinear singularities to all orders in perturbation theory[19].(b)Soft EmissionFor the emission of QCD radiation in the soft limit,a factorization theorem exists for the amplitude of the process.The amplitude for a process in which one gluon is much softer than the other energy scales in the process can be written as a product ofa universal eikonal current and the amplitude for the same process without the softgluon.After we square the amplitude and sum over the spins of the external partons, we obtain a result which depends on the momenta of all the external partons.It therefore seems unlikely that a Markov description based on sequential parton splittings can be recovered.The surprising result[20,21]is that,after azimuthal averaging,these eﬀects can be incorporated into a collinear algorithm by using the correct choice for the evolution scale,namely the opening angle.¯qgqFigure1:Feynman diagram and colourﬂow for e+e−→q¯q g.2.2.1Example:e+e−→q¯q ggWe can illustrate this with a simple example,i.e.the process e+e−→q¯q g1,shown in Fig.1.The semi-classical eikonal current can be used to study the emission of an extra soft gluon in this process,i.e.the process e+e−→q¯q g1g2where the second gluon is muchsofter than the other partons.The matrix element including the emission of the extra soft gluon is given byM(k1,k2,p1,p2,p3;q)=g s m(k1,k2,p1,p2,p3)·J(q)(5) where•m(k1,k2,p1,p2,p3)is the tree-level amplitude for the underlying process, e+(k1)e−(k2)→q(p1)¯q(p2)g1(p3).•M(k1,k2,p1,p2,p3;q)is the matrix element for the process e+(k1)e−(k2)→q(p1)¯q(p2)g1(p3)g2(q),i.e.including the emission of an extra soft gluon,g2,with momentum q.•J(q)is the non-Abelian semi-classical current for the emission of the soft gluon with momentum q,from the hard partons.•g s is the strong coupling constant.Explicitly in our example,the current,J(q),is given by[21]J(q)= s=1,2J b,µ(q)εµ,s,(6) whereεµ,s is the polarization vector of the gluon andJ b,µ(q)=t b,qc1c′1t ac′1c2 pµ1p2·q+if aa′b t a′c1c2 pµ3ω2W ij(Ωq)≡− p i p j·q 2=2ξiξj−12γ2jξ2j (8) where•ωis the energy of the soft gluon,•ξij=p i·p j•γi=E i/m i=1/ω2W(Ωq)(9) where C m is the colour factor for the tree-level process,and W(Ωq)the radiation pattern, given below in terms of the dipole radiation functions.For the process e+e−→q¯q g the colour factor C m=C F N c and the radiation pattern is given byW q¯q g(Ωq)=C A[W qg(Ωq)+W¯q g(Ωq)]−12N c and C A=N c are the Casimirs of the fundamental and adjoint rep-resentations respectively,with an arbitrary number of colours N c.This corresponds to emission of the soft gluon from colour dipoles,i.e.W qg is emission from the dipole formed by the quark and the anticolour line of the gluon,W¯q g emission from the colour line of the gluon and the antiquark and W q¯q emission from the quark and antiquark.Note that the q¯q dipole is negative which is a problem if we wish to use a probabilistic approach to treat the soft gluon radiation.The dipole radiation function can then be split into two parts as was done in[22],i.e.W ij(Ωq)=W i ij(Ωq)+W j ij(Ωq)(11)whereW i ij=1γ2iξi+ξij−ξiThis allows us to rewrite the square of the current,Eqn.7,in the following form,using these radiation functions,asW q¯q g(Ωq)=2C F W q qg+W¯q¯q g +C A W g g¯q+W g gq+N−1c W q qg−W q q¯q+W¯q¯q g−W¯q¯q q ,(13) which should be inserted in Eqn.9.This gives our main result in this example.The last term in Eqn.13,and other terms of this type,can be neglected as it is suppressed by 1/N2c with respect to the leading order term,as C F,C A∝N c,and is also dynamically suppressed as it does not contain a collinear singularity in the massless limit(e.g.the singularity in the quark direction cancels between the W q qg and W q q¯q terms.)Thus part of our approximation for the parton shower will consist of dropping the1/N2c terms.Colour Connected PartonsWe can now deﬁne the concept of the colour connected parton.Two partons are considered to be colour connected if they share the same colour line.The colourﬂow,in the large N c limit,for the process e+e−→q¯q g is shown in Fig.1with a dashed and a solid line.Thus the¯q and g are colour connected and the q and g are colour connected,while the¯q and q are not colour connected.Each quark only has one colour connected partner in a given Standard Model Feynman diagram and each gluon has two.Colour connected partners are deﬁned at each stage of the iterative parton showering procedure.If theﬁnal state q were to emit another gluon,g2,the newﬁnal state q would be colour connected to g2and no longer to g.g and g2would then also be colour connected.Angular Ordered Emission and Colour CoherenceWe see from Eqn.13that neglecting theﬁnal term,using the properties of the function W i ij,and averaging over the azimuthal angle of the gluon about a parton,the radiation can only occur in a cone about the direction of the parton up to the direction of its colour partner.This is shown in Fig.2.We can draw a cone around parton one with half-angle given by the angle between the momenta of partons one and two.The emission from parton one within the cone deﬁned by its colour connected partner,parton two,is called angular ordered emission.The angular ordering procedure is one way of implementing the phenomenon of colour coherence.The idea of colour coherence is that if we consider a large angle gluon it can only resolve the total colour charge of a pair of smaller angle partons,and not their individual charges.It is therefore as if the larger-angle soft gluon was emitted before the smaller angle branchings.There have been a number of experimental studies of colour coherence eﬀects.In particular the string eﬀect in e+e−collisions[23],where there is a suppression of soft QCD radiation between the two quark jets in three jet events.There have also been studies of colour coherence eﬀects between the initial andﬁnal states in hadron-hadron collisions,[24,25].It is nowﬁrmly established that event generators that do not incorporate colour coherence cannot reliably predict the hadronicﬁnal state.Although we have averaged over the azimuthal angle of the emission of the gluon in both the soft and collinear cases,azimuthal eﬀects,e.g.due to spin correlations,can be included[26],after the full parton shower has been generated.2.2.2Non-Planar Colour FlowsWe have explained in an example how the cross section for n+1partons factorizes in both the collinear and soft limits into a universal splitting term and the cross section for n partons.Both of these limits can be implemented by using angles as the evolution variable in a Markov branching procedure.We start at the hard cross section,normally with a two-to-two process.The maximum angle of emission from a parton is set by the direction of the colour partner.We then generate some smaller angle parton,e.g.a gluon from a quark.Then we repeat the procedure,i.e.the gluon’s colour partner is now the colour partner of the original quark,and its anticolour partner the quark,and the colour partner of the quark is the gluon.One of the partons will radiate with the maximum angle given by the direction of the new colour partner and so on until the cut-oﬀis reached,of order1GeV,below which emission does not occur.This procedure then resums both the leading soft and collinear singularities.In processes where there is more than one Feynman diagram it is possible for the colourﬂows in the diagrams to be diﬀerent.This leads to so called‘non-planar’terms from the interference terms,where the colourﬂows do not match.These are not positive deﬁnite and hence cannot be interpreted in a probabilistic way for implementation in the Monte Carlo procedure.They are always suppressed by inverse powers of N c.A procedure must be adopted to split up the‘non-planar’parts of the tree-level matrix element to give redeﬁned planar terms with positive-deﬁnite coeﬃcients that can be used in the Monte Carlo procedure.Such a procedure was proposed in[21]and shown to work correctly for all QCD processes.However,as shown in[27],this is inadequate for MSSM processes and hence a new procedure was proposed,which we adopt here.In this procedure the ‘non-planar’parts of the matrix element are split up according to|M|2i|M|2planarM|2i is the matrix element squared for the i th colourﬂow,|M|2tot is the total matrix element squared.This ensures that the terms are positive deﬁnite and the new full planar terms have the correct pole structure and sum to the correct total cross section.This can then be implemented numerically.1.Direction of parton2.Direction of thecolour partnerFigure2:Emission in angular ordered cones.In this section we have explained how by using a Markov branching procedure we can resum both the soft and collinear singularities in QCD.2.3HadronizationAfter the parton shower phase it is necessary to adopt some procedure to combine the quarks and gluons into the observed hadrons.This is done in the HERWIG event generator using the cluster hadronization model[28].This model is based on the concept of colour preconﬁnement.This implies that the invariant mass of pairs of colour-connected partons has a spectrum that is peaked at low values,a few times the cut-oﬀused in the parton-shower,and is universal,i.e.independent of the hard scale and type of the collision,as discussed below and shown in Fig.11a.In the cluster hadronization model[28],after the end of the parton showering process we are left with gluons and quarks.The gluons are non-perturbatively split into light quark-antiquark pairs.Theﬁnal state then consists only of quarks and antiquarks which are,in the planar approximation,uniquely paired in colour-anticolour pairs.These pairs of colour-connected quarks do not necessarily have the correct invariant mass to form a meson.Instead they are formed into colour-singlet meson-like resonance called‘clusters’. These clusters then decay in their rest frame to a pair of hadrons(either two mesons or a baryon and an antibaryon)with the type of hadron determined by the available phase space.In the original model of[28]these decays were isotropic in the rest frame of the cluster,however in the current implementation of the model[17],the hadrons containing the quarks from the perturbative stage of the event continue in the same direction(in the cluster rest frame)as the original quark.It is reasonable to assume that the low mass clusters are superpositions of hadron resonances and can be treated in this way[28].However,a fraction of the clusters have higher masses for which this assumption is not valid and these clusters areﬁrst split using a string-like mechanism[28]into lighter clusters before they are decayed to hadrons.A simple extension of this model is used for hadron remnants.For example in a collision in which a valence quark from a proton participates in a hard process,the two remaining valence quarks are left in theﬁnal state.They are paired up as a‘diquark’which,in the planar approximation,carries an anticolour index and can be treated like an antiquark.The resulting cluster has baryonic quantum numbers and decays into a baryon and a meson.3Angular Ordering in R pIn Standard Model and MSSM processes apart from complications involving processes where there are‘non-planar’terms[27]the angular ordering procedure is relatively straight-forward to implement.However in R p SUSY there are additional complications.The lepton number violating processes,which come from theﬁrst two terms in the superpotential,Eqn.2,have colourﬂows that are the same as those which occur in the MSSM.On the other hand the baryon number violating interactions,which come from the third term in Eqn.2,have a very diﬀerent colour structure involving the totally an-tisymmetric tensor,ǫc1c2c3.We lookﬁrst at the colour structure of the various baryon number violating decays which we include in the Monte Carlo simulation and then at the structure of the various hard scattering processes.3.1DecaysFrom the point of view of the colour structure there are three types of baryon number violating decays which we include in the Monte Carlo simulation.1.Two-body B decay of an antisquark to two quarks or a squark to two antiquarks.2.Three-body B decay of a colourless sparticle,i.e.a neutralino or a chargino,to threequarks or antiquarks.3.Three-body B decay of the gluino to three quarks or antiquarks.In general it is possible to consider for example the decay of a neutralino to three quarks as either a three-body decay or two sequential two-body decays,of the neutralino to an antisquark and a quark and then of the antisquark to two quarks.If either of the two sequential two-body decays are kinematically forbidden,i.e.they can only proceed if the internal particle in the three-body decay is oﬀ-shell,then we consider the decay to be three-body,otherwise we treat the decay as two sequential two-body decays.The problem is then how to implement the angular ordering procedure for these three processes.We shall consider them using the eikonal current with an arbitrary number of colours as was done in Section2.2.1for the process e+e−→q¯q g.So in these R-parity violating processes this means we need to consider the decay of an antisquark to(N c−1)quarks and of the neutralino,chargino and gluino to N c quarks.We also have to use the generalization to N c colours of the antisymmetric tensor,i.e.ǫc1...c N c.3.1.1Squark DecaysFor the decay of an antisquark to(N c−1)quarks the leading infrared contribution to the soft gluon distribution has the following factorized form.M(p0,p1,p2,...,p Nc−1;q)=g s m(p0,p1,p2,...,p Nc−1)·J(q)(15)where•m(p0,p1,p2,...,p N c−1)is the tree-level matrix element for an antisquark,with mo-mentum p0,to decay to N c−1quarks,with momentum p1,...,p N c−1.•M(p0,p1,p2,...,p N c−1;q)is the tree-level matrix element for the decay of an anti-squark to N c−1quarks including the emission of an extra soft gluon,with momen-tum q.•J(q)is the non-Abelian semi-classical current for the emission of the soft gluon with momentum q from the hard partons.•c 0is the colour of the decaying antisquark and c 1,...c N c −1are the colours of the quarks.Again the current,J (q ),is given by,J (q )= s =1,2J b,µ(q )εµ,s where hereJ b,µ(q )=− p µ0p i ·q t b,q i c i ,c ′iǫc 0,...,c ′i ,...,c N c −1.(16)b and µare the colour and Lorentz indices of the emitted gluon;t b,˜q ∗,t b,q i are the colourmatrices of the antisquark and quarks,respectively.We obtain the soft gluon distribution simply by squaring the currentJ 2(q )=−C F N c (N c −2)! N c −1 i =1 p 0p i ·q 2+N c −1 i =1N c −1 j>ip i p j ·q 2 .(17)This can be expressed in terms of the radiation functions as in Eqn.9,where here the tree-level colour factor is C m =ǫc 0,...,c N c −1ǫc 0,...,c N c −1=N c !,where we have not averaged over the initial colours,and the radiation pattern is given byW (Ωq )=−ω2C Fp 0·q −p ip i ·q −p j(N c −1)N c −1 i =0N c −1 j =i W i ij .(19)This is exactly the same result obtained in [29],in the context of baryon number violation in the Standard Model,except that the massless radiation functions of their paper are now replaced by the massive functions here.This leads to the following approach for treating the soft gluon radiation from this process.The quarks from the decay are randomly colour connected to either the decaying antisquark or the other quark.This then correctly treats the soft gluon radiation from the decay products.In general,the QCD radiation from sparticles,which are here in the initial state,is neglected in HERWIG.We would expect this approximation to be valid for two reasons,ﬁrstly the sparticles will usually have a short lifetime and secondly,due to their heavy masses the QCD radiation will also be suppressed unless they have momenta much greater than their masses.However for the decays we consider,we can include the eﬀects of radiation from the decaying sparticles.This is done by treating the radiation in the rest frame of the decaying squark where there is no radiation from the decaying sparticle,which HERWIG would not generate anyway.However as stated in Section 2.2.1while theradiation from individual partons,i.e.W i ij ,is not Lorentz invariant the dipole radiationfunctions are.Hence the total radiation pattern is Lorentz invariant and therefore by treating the decay in the rest frame of the decaying particle we correctly include the QCD radiation from the decaying particle when we boost back to the lab frame.3.1.2Chargino and Neutralino DecaysThe charginos decay via the process shown in Fig.3,and the neutralinos via the process in Fig.4.If we consider the QCD radiation from the decay of a colour neutral object which decays,for an arbitrary number of colours N c,to N c quarks,then we see that there is only one possible colourﬂow for this process.The squarks appearing in these processes,˜q iα, can be either of the statesα=1,2resulting from the mixing of˜q iL and˜q iR,as discussed in more detail in the appendix.Figure3:UDD decays of the˜χ+.In fact,the colour structure of this process is very similar to that of the squark decay and the matrix element in the soft limit can be written in the same factorized form as before.Again,we can express the current as in Eqn.9where the tree-level colour factor C m=ǫc0,...,c N c−1ǫc0,...,c N c−1=N c!and the radiation function is given by2C FW(Ωq)=3.1.3Gluino DecaysThe colour structure of the gluino decay is very diﬀerent from that of the colourless objects or the squarks which we have already considered,the diagrams for this process are shown in Fig.5.Again if we consider an arbitrary number of colours,N c ,the gluino will decay to N c quarks.In this case there will be N c possible colour ﬂows,corresponding to the Feynman diagrams and colour ﬂows shown in Fig.6.These diﬀerent colour ﬂows will lead to ‘non-planar’terms which must be dealt with.Figure 5:UDD decays of the ˜g .The leading infrared contribution to the soft gluon distribution can be written in the following factorized form.M (p 0,p 1,p 2,...,p N c ;q )=g sN c i =1m i (p 0,p 1,p 2,...,p N c )·J i (q )(21)where •m i (p 0,p 1,p 2,...,p N c )is the tree-level matrix element of the three-body gluino decayfor the i th possible colour ﬂow.•M (p 0,p 1,p 2,...,p N c ;q )is the tree-level matrix element for the three-body gluinodecay including the extra emission of a soft gluon of momentum q .•J i (q )is the non-Abelian semi-classical current for the emission of the soft gluon,momentum q ,from the hard partons for the i th possible colour ﬂow.Again the current has the form J i (q )= s =1,2J b,µi (q )εµ,s ,where in this caseJ b,µi (q )=i p µp i ·qt b c i c ′i t a c ′i c ′′i ǫc 1...c ′′i ...c N c +N c j =1,j =ip µj。

$Zto bbar b$ in $U(1)_R$ Symmetric Supersymmetry

which yield a value (Rb )exp = 0.2205 ± 0.0016 [4] that diﬀers markedly from the one-loop standard model prediction (Rb )SM = 0.2158, (mt = 174GeV) [5]. The oblique and QCD corrections to the b-quark and hadronic decay widths of the Z each largely cancel when the ratio is formed, making Rb very sensitive to direct corrections to the Zb¯ b vertex – especially those involving the heavy top quark. Our work complements some recent papers on SUSY models with discrete R-parity. The implications of the Rb measurement for the MSSM are discussed in refs. [6], [7] and [8]. A region of the MSSM parameter space that has some phenomenology similar to that of the MR model is studied in [9]. The following section describes the MR model in more detail. We then compute the vertex corrections to Rb in the MR model and ﬁnd that the result is within 2σ of the experimental value so long as the lighter top squark is light enough (and the charged Higgs boson is heavy enough). Section 4 discusses additional constraints that place a lower bound on the mass of the lighter top squark. The information that future experiments may yield is studied in section 5; ongoing and upcoming experiments at FNAL and LEP should be capable of conﬁrming or excluding the MR model. The last section brieﬂy summarizes our ﬁndings. 1

OSHA现场作业手册说明书

DIRECTIVE NUMBER: CPL 02-00-150 EFFECTIVE DATE: April 22, 2011 SUBJECT: Field Operations Manual (FOM)ABSTRACTPurpose: This instruction cancels and replaces OSHA Instruction CPL 02-00-148,Field Operations Manual (FOM), issued November 9, 2009, whichreplaced the September 26, 1994 Instruction that implemented the FieldInspection Reference Manual (FIRM). The FOM is a revision of OSHA’senforcement policies and procedures manual that provides the field officesa reference document for identifying the responsibilities associated withthe majority of their inspection duties. This Instruction also cancels OSHAInstruction FAP 01-00-003 Federal Agency Safety and Health Programs,May 17, 1996 and Chapter 13 of OSHA Instruction CPL 02-00-045,Revised Field Operations Manual, June 15, 1989.Scope: OSHA-wide.References: Title 29 Code of Federal Regulations §1903.6, Advance Notice ofInspections; 29 Code of Federal Regulations §1903.14, Policy RegardingEmployee Rescue Activities; 29 Code of Federal Regulations §1903.19,Abatement Verification; 29 Code of Federal Regulations §1904.39,Reporting Fatalities and Multiple Hospitalizations to OSHA; and Housingfor Agricultural Workers: Final Rule, Federal Register, March 4, 1980 (45FR 14180).Cancellations: OSHA Instruction CPL 02-00-148, Field Operations Manual, November9, 2009.OSHA Instruction FAP 01-00-003, Federal Agency Safety and HealthPrograms, May 17, 1996.Chapter 13 of OSHA Instruction CPL 02-00-045, Revised FieldOperations Manual, June 15, 1989.State Impact: Notice of Intent and Adoption required. See paragraph VI.Action Offices: National, Regional, and Area OfficesOriginating Office: Directorate of Enforcement Programs Contact: Directorate of Enforcement ProgramsOffice of General Industry Enforcement200 Constitution Avenue, NW, N3 119Washington, DC 20210202-693-1850By and Under the Authority ofDavid Michaels, PhD, MPHAssistant SecretaryExecutive SummaryThis instruction cancels and replaces OSHA Instruction CPL 02-00-148, Field Operations Manual (FOM), issued November 9, 2009. The one remaining part of the prior Field Operations Manual, the chapter on Disclosure, will be added at a later date. This Instruction also cancels OSHA Instruction FAP 01-00-003 Federal Agency Safety and Health Programs, May 17, 1996 and Chapter 13 of OSHA Instruction CPL 02-00-045, Revised Field Operations Manual, June 15, 1989. This Instruction constitutes OSHA’s general enforcement policies and procedures manual for use by the field offices in conducting inspections, issuing citations and proposing penalties.Significant Changes∙A new Table of Contents for the entire FOM is added.∙ A new References section for the entire FOM is added∙ A new Cancellations section for the entire FOM is added.∙Adds a Maritime Industry Sector to Section III of Chapter 10, Industry Sectors.∙Revises sections referring to the Enhanced Enforcement Program (EEP) replacing the information with the Severe Violator Enforcement Program (SVEP).∙Adds Chapter 13, Federal Agency Field Activities.∙Cancels OSHA Instruction FAP 01-00-003, Federal Agency Safety and Health Programs, May 17, 1996.DisclaimerThis manual is intended to provide instruction regarding some of the internal operations of the Occupational Safety and Health Administration (OSHA), and is solely for the benefit of the Government. No duties, rights, or benefits, substantive or procedural, are created or implied by this manual. The contents of this manual are not enforceable by any person or entity against the Department of Labor or the United States. Statements which reflect current Occupational Safety and Health Review Commission or court precedents do not necessarily indicate acquiescence with those precedents.Table of ContentsCHAPTER 1INTRODUCTIONI.PURPOSE. ........................................................................................................... 1-1 II.SCOPE. ................................................................................................................ 1-1 III.REFERENCES .................................................................................................... 1-1 IV.CANCELLATIONS............................................................................................. 1-8 V. ACTION INFORMATION ................................................................................. 1-8A.R ESPONSIBLE O FFICE.......................................................................................................................................... 1-8B.A CTION O FFICES. .................................................................................................................... 1-8C. I NFORMATION O FFICES............................................................................................................ 1-8 VI. STATE IMPACT. ................................................................................................ 1-8 VII.SIGNIFICANT CHANGES. ............................................................................... 1-9 VIII.BACKGROUND. ................................................................................................. 1-9 IX. DEFINITIONS AND TERMINOLOGY. ........................................................ 1-10A.T HE A CT................................................................................................................................................................. 1-10B. C OMPLIANCE S AFETY AND H EALTH O FFICER (CSHO). ...........................................................1-10B.H E/S HE AND H IS/H ERS ..................................................................................................................................... 1-10C.P ROFESSIONAL J UDGMENT............................................................................................................................... 1-10E. W ORKPLACE AND W ORKSITE ......................................................................................................................... 1-10CHAPTER 2PROGRAM PLANNINGI.INTRODUCTION ............................................................................................... 2-1 II.AREA OFFICE RESPONSIBILITIES. .............................................................. 2-1A.P ROVIDING A SSISTANCE TO S MALL E MPLOYERS. ...................................................................................... 2-1B.A REA O FFICE O UTREACH P ROGRAM. ............................................................................................................. 2-1C. R ESPONDING TO R EQUESTS FOR A SSISTANCE. ............................................................................................ 2-2 III. OSHA COOPERATIVE PROGRAMS OVERVIEW. ...................................... 2-2A.V OLUNTARY P ROTECTION P ROGRAM (VPP). ........................................................................... 2-2B.O NSITE C ONSULTATION P ROGRAM. ................................................................................................................ 2-2C.S TRATEGIC P ARTNERSHIPS................................................................................................................................. 2-3D.A LLIANCE P ROGRAM ........................................................................................................................................... 2-3 IV. ENFORCEMENT PROGRAM SCHEDULING. ................................................ 2-4A.G ENERAL ................................................................................................................................................................. 2-4B.I NSPECTION P RIORITY C RITERIA. ..................................................................................................................... 2-4C.E FFECT OF C ONTEST ............................................................................................................................................ 2-5D.E NFORCEMENT E XEMPTIONS AND L IMITATIONS. ....................................................................................... 2-6E.P REEMPTION BY A NOTHER F EDERAL A GENCY ........................................................................................... 2-6F.U NITED S TATES P OSTAL S ERVICE. .................................................................................................................. 2-7G.H OME-B ASED W ORKSITES. ................................................................................................................................ 2-8H.I NSPECTION/I NVESTIGATION T YPES. ............................................................................................................... 2-8 V.UNPROGRAMMED ACTIVITY – HAZARD EVALUATION AND INSPECTION SCHEDULING ............................................................................ 2-9 VI.PROGRAMMED INSPECTIONS. ................................................................... 2-10A.S ITE-S PECIFIC T ARGETING (SST) P ROGRAM. ............................................................................................. 2-10B.S CHEDULING FOR C ONSTRUCTION I NSPECTIONS. ..................................................................................... 2-10C.S CHEDULING FOR M ARITIME I NSPECTIONS. ............................................................................. 2-11D.S PECIAL E MPHASIS P ROGRAMS (SEP S). ................................................................................... 2-12E.N ATIONAL E MPHASIS P ROGRAMS (NEP S) ............................................................................... 2-13F.L OCAL E MPHASIS P ROGRAMS (LEP S) AND R EGIONAL E MPHASIS P ROGRAMS (REP S) ............ 2-13G.O THER S PECIAL P ROGRAMS. ............................................................................................................................ 2-13H.I NSPECTION S CHEDULING AND I NTERFACE WITH C OOPERATIVE P ROGRAM P ARTICIPANTS ....... 2-13CHAPTER 3INSPECTION PROCEDURESI.INSPECTION PREPARATION. .......................................................................... 3-1 II.INSPECTION PLANNING. .................................................................................. 3-1A.R EVIEW OF I NSPECTION H ISTORY .................................................................................................................... 3-1B.R EVIEW OF C OOPERATIVE P ROGRAM P ARTICIPATION .............................................................................. 3-1C.OSHA D ATA I NITIATIVE (ODI) D ATA R EVIEW .......................................................................................... 3-2D.S AFETY AND H EALTH I SSUES R ELATING TO CSHO S.................................................................. 3-2E.A DVANCE N OTICE. ................................................................................................................................................ 3-3F.P RE-I NSPECTION C OMPULSORY P ROCESS ...................................................................................................... 3-5G.P ERSONAL S ECURITY C LEARANCE. ................................................................................................................. 3-5H.E XPERT A SSISTANCE. ........................................................................................................................................... 3-5 III. INSPECTION SCOPE. ......................................................................................... 3-6A.C OMPREHENSIVE ................................................................................................................................................... 3-6B.P ARTIAL. ................................................................................................................................................................... 3-6 IV. CONDUCT OF INSPECTION .............................................................................. 3-6A.T IME OF I NSPECTION............................................................................................................................................. 3-6B.P RESENTING C REDENTIALS. ............................................................................................................................... 3-6C.R EFUSAL TO P ERMIT I NSPECTION AND I NTERFERENCE ............................................................................. 3-7D.E MPLOYEE P ARTICIPATION. ............................................................................................................................... 3-9E.R ELEASE FOR E NTRY ............................................................................................................................................ 3-9F.B ANKRUPT OR O UT OF B USINESS. .................................................................................................................... 3-9G.E MPLOYEE R ESPONSIBILITIES. ................................................................................................. 3-10H.S TRIKE OR L ABOR D ISPUTE ............................................................................................................................. 3-10I. V ARIANCES. .......................................................................................................................................................... 3-11 V. OPENING CONFERENCE. ................................................................................ 3-11A.G ENERAL ................................................................................................................................................................ 3-11B.R EVIEW OF A PPROPRIATION A CT E XEMPTIONS AND L IMITATION. ..................................................... 3-13C.R EVIEW S CREENING FOR P ROCESS S AFETY M ANAGEMENT (PSM) C OVERAGE............................. 3-13D.R EVIEW OF V OLUNTARY C OMPLIANCE P ROGRAMS. ................................................................................ 3-14E.D ISRUPTIVE C ONDUCT. ...................................................................................................................................... 3-15F.C LASSIFIED A REAS ............................................................................................................................................. 3-16VI. REVIEW OF RECORDS. ................................................................................... 3-16A.I NJURY AND I LLNESS R ECORDS...................................................................................................................... 3-16B.R ECORDING C RITERIA. ...................................................................................................................................... 3-18C. R ECORDKEEPING D EFICIENCIES. .................................................................................................................. 3-18 VII. WALKAROUND INSPECTION. ....................................................................... 3-19A.W ALKAROUND R EPRESENTATIVES ............................................................................................................... 3-19B.E VALUATION OF S AFETY AND H EALTH M ANAGEMENT S YSTEM. ....................................................... 3-20C.R ECORD A LL F ACTS P ERTINENT TO A V IOLATION. ................................................................................. 3-20D.T ESTIFYING IN H EARINGS ................................................................................................................................ 3-21E.T RADE S ECRETS. ................................................................................................................................................. 3-21F.C OLLECTING S AMPLES. ..................................................................................................................................... 3-22G.P HOTOGRAPHS AND V IDEOTAPES.................................................................................................................. 3-22H.V IOLATIONS OF O THER L AWS. ....................................................................................................................... 3-23I.I NTERVIEWS OF N ON-M ANAGERIAL E MPLOYEES .................................................................................... 3-23J.M ULTI-E MPLOYER W ORKSITES ..................................................................................................................... 3-27 K.A DMINISTRATIVE S UBPOENA.......................................................................................................................... 3-27 L.E MPLOYER A BATEMENT A SSISTANCE. ........................................................................................................ 3-27 VIII. CLOSING CONFERENCE. .............................................................................. 3-28A.P ARTICIPANTS. ..................................................................................................................................................... 3-28B.D ISCUSSION I TEMS. ............................................................................................................................................ 3-28C.A DVICE TO A TTENDEES .................................................................................................................................... 3-29D.P ENALTIES............................................................................................................................................................. 3-30E.F EASIBLE A DMINISTRATIVE, W ORK P RACTICE AND E NGINEERING C ONTROLS. ............................ 3-30F.R EDUCING E MPLOYEE E XPOSURE. ................................................................................................................ 3-32G.A BATEMENT V ERIFICATION. ........................................................................................................................... 3-32H.E MPLOYEE D ISCRIMINATION .......................................................................................................................... 3-33 IX. SPECIAL INSPECTION PROCEDURES. ...................................................... 3-33A.F OLLOW-UP AND M ONITORING I NSPECTIONS............................................................................................ 3-33B.C ONSTRUCTION I NSPECTIONS ......................................................................................................................... 3-34C. F EDERAL A GENCY I NSPECTIONS. ................................................................................................................. 3-35CHAPTER 4VIOLATIONSI. BASIS OF VIOLATIONS ..................................................................................... 4-1A.S TANDARDS AND R EGULATIONS. .................................................................................................................... 4-1B.E MPLOYEE E XPOSURE. ........................................................................................................................................ 4-3C.R EGULATORY R EQUIREMENTS. ........................................................................................................................ 4-6D.H AZARD C OMMUNICATION. .............................................................................................................................. 4-6E. E MPLOYER/E MPLOYEE R ESPONSIBILITIES ................................................................................................... 4-6 II. SERIOUS VIOLATIONS. .................................................................................... 4-8A.S ECTION 17(K). ......................................................................................................................... 4-8B.E STABLISHING S ERIOUS V IOLATIONS ............................................................................................................ 4-8C. F OUR S TEPS TO BE D OCUMENTED. ................................................................................................................... 4-8 III. GENERAL DUTY REQUIREMENTS ............................................................. 4-14A.E VALUATION OF G ENERAL D UTY R EQUIREMENTS ................................................................................. 4-14B.E LEMENTS OF A G ENERAL D UTY R EQUIREMENT V IOLATION.............................................................. 4-14C. U SE OF THE G ENERAL D UTY C LAUSE ........................................................................................................ 4-23D.L IMITATIONS OF U SE OF THE G ENERAL D UTY C LAUSE. ..............................................................E.C LASSIFICATION OF V IOLATIONS C ITED U NDER THE G ENERAL D UTY C LAUSE. ..................F. P ROCEDURES FOR I MPLEMENTATION OF S ECTION 5(A)(1) E NFORCEMENT ............................ 4-25 4-27 4-27IV.OTHER-THAN-SERIOUS VIOLATIONS ............................................... 4-28 V.WILLFUL VIOLATIONS. ......................................................................... 4-28A.I NTENTIONAL D ISREGARD V IOLATIONS. ..........................................................................................4-28B.P LAIN I NDIFFERENCE V IOLATIONS. ...................................................................................................4-29 VI. CRIMINAL/WILLFUL VIOLATIONS. ................................................... 4-30A.A REA D IRECTOR C OORDINATION ....................................................................................................... 4-31B.C RITERIA FOR I NVESTIGATING P OSSIBLE C RIMINAL/W ILLFUL V IOLATIONS ........................ 4-31C. W ILLFUL V IOLATIONS R ELATED TO A F ATALITY .......................................................................... 4-32 VII. REPEATED VIOLATIONS. ...................................................................... 4-32A.F EDERAL AND S TATE P LAN V IOLATIONS. ........................................................................................4-32B.I DENTICAL S TANDARDS. .......................................................................................................................4-32C.D IFFERENT S TANDARDS. .......................................................................................................................4-33D.O BTAINING I NSPECTION H ISTORY. .....................................................................................................4-33E.T IME L IMITATIONS..................................................................................................................................4-34F.R EPEATED V. F AILURE TO A BATE....................................................................................................... 4-34G. A REA D IRECTOR R ESPONSIBILITIES. .............................................................................. 4-35 VIII. DE MINIMIS CONDITIONS. ................................................................... 4-36A.C RITERIA ................................................................................................................................................... 4-36B.P ROFESSIONAL J UDGMENT. ..................................................................................................................4-37C. A REA D IRECTOR R ESPONSIBILITIES. .............................................................................. 4-37 IX. CITING IN THE ALTERNATIVE ............................................................ 4-37 X. COMBINING AND GROUPING VIOLATIONS. ................................... 4-37A.C OMBINING. ..............................................................................................................................................4-37B.G ROUPING. ................................................................................................................................................4-38C. W HEN N OT TO G ROUP OR C OMBINE. ................................................................................................4-38 XI. HEALTH STANDARD VIOLATIONS ....................................................... 4-39A.C ITATION OF V ENTILATION S TANDARDS ......................................................................................... 4-39B.V IOLATIONS OF THE N OISE S TANDARD. ...........................................................................................4-40 XII. VIOLATIONS OF THE RESPIRATORY PROTECTION STANDARD(§1910.134). ....................................................................................................... XIII. VIOLATIONS OF AIR CONTAMINANT STANDARDS (§1910.1000) ... 4-43 4-43A.R EQUIREMENTS UNDER THE STANDARD: .................................................................................................. 4-43B.C LASSIFICATION OF V IOLATIONS OF A IR C ONTAMINANT S TANDARDS. ......................................... 4-43 XIV. CITING IMPROPER PERSONAL HYGIENE PRACTICES. ................... 4-45A.I NGESTION H AZARDS. .................................................................................................................................... 4-45B.A BSORPTION H AZARDS. ................................................................................................................................ 4-46C.W IPE S AMPLING. ............................................................................................................................................. 4-46D.C ITATION P OLICY ............................................................................................................................................ 4-46 XV. BIOLOGICAL MONITORING. ...................................................................... 4-47CHAPTER 5CASE FILE PREPARATION AND DOCUMENTATIONI.INTRODUCTION ............................................................................................... 5-1 II.INSPECTION CONDUCTED, CITATIONS BEING ISSUED. .................... 5-1A.OSHA-1 ................................................................................................................................... 5-1B.OSHA-1A. ............................................................................................................................... 5-1C. OSHA-1B. ................................................................................................................................ 5-2 III.INSPECTION CONDUCTED BUT NO CITATIONS ISSUED .................... 5-5 IV.NO INSPECTION ............................................................................................... 5-5 V. HEALTH INSPECTIONS. ................................................................................. 5-6A.D OCUMENT P OTENTIAL E XPOSURE. ............................................................................................................... 5-6B.E MPLOYER’S O CCUPATIONAL S AFETY AND H EALTH S YSTEM. ............................................................. 5-6 VI. AFFIRMATIVE DEFENSES............................................................................. 5-8A.B URDEN OF P ROOF. .............................................................................................................................................. 5-8B.E XPLANATIONS. ..................................................................................................................................................... 5-8 VII. INTERVIEW STATEMENTS. ........................................................................ 5-10A.G ENERALLY. ......................................................................................................................................................... 5-10B.CSHO S SHALL OBTAIN WRITTEN STATEMENTS WHEN: .......................................................................... 5-10C.L ANGUAGE AND W ORDING OF S TATEMENT. ............................................................................................. 5-11D.R EFUSAL TO S IGN S TATEMENT ...................................................................................................................... 5-11E.V IDEO AND A UDIOTAPED S TATEMENTS. ..................................................................................................... 5-11F.A DMINISTRATIVE D EPOSITIONS. .............................................................................................5-11 VIII. PAPERWORK AND WRITTEN PROGRAM REQUIREMENTS. .......... 5-12 IX.GUIDELINES FOR CASE FILE DOCUMENTATION FOR USE WITH VIDEOTAPES AND AUDIOTAPES .............................................................. 5-12 X.CASE FILE ACTIVITY DIARY SHEET. ..................................................... 5-12 XI. CITATIONS. ..................................................................................................... 5-12A.S TATUTE OF L IMITATIONS. .............................................................................................................................. 5-13B.I SSUING C ITATIONS. ........................................................................................................................................... 5-13C.A MENDING/W ITHDRAWING C ITATIONS AND N OTIFICATION OF P ENALTIES. .................................. 5-13D.P ROCEDURES FOR A MENDING OR W ITHDRAWING C ITATIONS ............................................................ 5-14 XII. INSPECTION RECORDS. ............................................................................... 5-15A.G ENERALLY. ......................................................................................................................................................... 5-15B.R ELEASE OF I NSPECTION I NFORMATION ..................................................................................................... 5-15C. C LASSIFIED AND T RADE S ECRET I NFORMATION ...................................................................................... 5-16。

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a r X i v :h e p -p h /9703436v 2 8 A p r 1997BI-TP 97/08DESY 97-044WUE-ITP-97-04hep-ph/9703436Supersymmetry with R -Parity Breaking:Contact Interactions and Resonance Formationin Leptonic Processes at LEP2J.Kalinowski 1,2,R.R¨u ckl 3,∗,H.Spiesberger 4,∗,and P.M.Zerwas 11Deutsches Elektronen-Synchrotron DESY,D-22607Hamburg2Institute of Theoretical Physics,Warsaw University,PL-00681Warsaw3Institut f¨u r Theoretische Physik,Universit¨a t W¨u rzburg,D-97074W¨u rzburg4Fakult¨a t f¨u r Physik,Universit¨a t Bielefeld,D-33501BielefeldABSTRACTIn supersymmetric theories with R -parity breaking,trilinear couplings of two leptons to scalar sleptons are possible.In electron–positron collisions such interactions would manifest themselves through contact terms in Bhabha scat-tering,e +e −→e +e −,and in annihilation to lepton pairs,e +e −→µ+µ−and τ+τ−.Interpreting the high x ,high Q 2DIS HERA events as charm squark pro-duction with squark masses of order 200GeV,the formation of tau -sneutrinos,e +e −→˜ντ,with a mass in the range close to the LEP2energy or even in reach,is an exciting speculation which can be investigated in the coming LEP2runs with energies close to√∗Supported by Bundesministerium f¨u r Bildung,Wissenschaft,Forschung und Technologie,Bonn,Ger-many,Contracts 057BI92P (9)and 057WZ91P (0).11IntroductionThe recent observation of surplus events in deep-inelastic positron–proton scattering at HERA at high x and high Q2above a priori expectations[1]has given rise to many speculations.If the surplus is not a statisticalﬂuctuation,an attractive interpretation is oﬀered by supersymmetry with R-parity breaking[2].Since in particular the H1events cluster at a mass value of200GeV,resonance squark production e+d→˜c,˜t could explain the HERA events1without spoiling the tremendous success of the high-precision analyses based on the Standard Model.In addition to the lepton-quark-quark superﬁeld term,the R-breaking part of the superpotential may involve also the interaction of three lepton superﬁelds[4,5]:W R/=λijk L i L L j L¯E k R+λ′ijk L i L Q j L¯D k R(1) Both couplingsλandλ′violate lepton number(L).Their coexistence is not excluded by the non-observation of proton decay.The indices ijk denote the generations;λijk are non-vanishing only for i<j so that at least two diﬀerent generations are coupled in the purely leptonic vertices.The standard notation is used in Eq.(1)for the left-handed doublets of leptons(L)and quarks(Q),and the right-handed singlets of charged leptons(E)and down-type quarks(D).In four-component Dirac notation,the lepton part of the Yukawa interactions has the following form:L l R/=λijk ˜νj L¯e k R e i L+(˜e k R)∗(¯e i L)cνj L+˜e i L¯e k Rνj L−˜νi L¯e k R e j L−(˜e k R)∗(¯e j L)cνi L−˜e j L¯e k Rνi L +h.c.(2) u i and d i denote the u-and d-type quarks,e i andνi the charged and neutral leptons,re-spectively;¯l denotes the spinor of the antiparticle,the superscript()c the charge conjugate spinor and()∗the complex conjugate scalar.The interpretation of the HERA events by R-parity breaking SUSY interactions in-volves at least one of the couplingsλ′,in the most attractive scenariosλ′121orλ′131,giving rise to charm or top squark production with masses∼200GeV,respectively.This invites to the speculation that some of the couplingsλmay also be non-zero in the purely lep-tonic sector and that other supersymmetric particles,sleptons,may exist in a similar mass range.A similar idea has been envisaged[6]in the charged slepton sector to account for the Aleph4-jet events[7].In the present paper we investigate sneutrino eﬀects in leptonic e+e−processes at the high energies2realized at LEP2.They include Bhabha scattering andℓ+ℓ−pair production:e+e−→e+e−(3)e+e−→µ+µ−,τ+τ−(4)Neutrino pair-production,involving the exchange of charged sleptons,can be analysed in the same way after obvious substitutions,though experimental analyses are much more diﬃcult.Both processes(3)and(4)can be aﬀected by the exchange of sneutrinos in the s-and/or t-channel.For sneutrinos with masses in the order of200GeV,the eﬀects can be quite signiﬁcant,depending on the size of the couplings.Even though there are strong upper bounds on several of theλcouplings,some of these couplings are rather unconstrained,in particular the coupling that violates only theτ-ﬂavor,so the eﬀects induced byτsneutrinos can be large.While contact interactions relevant for much heavier sneutrinos have been discussed earlier in the literature[9,10,11],we improve on these analyses by including the impact of nearby resonances;they require the proper account of sneutrino propagator and non-zero width eﬀects.Most exciting of course would be the direct formation of sneutrinos[10,11,12]e+e−→˜ντ(5) for sneutrino masses in the LEP2range.The sneutrinos would manifest themselves as a sharp resonance peak.2Slepton Exchange in e+e−CollisionsAt energies much lower than the sparticle masses,R-parity breaking interactions introduce eﬀective llll and llqq contact interactions.These operators will in general mediate L violating processes and FCNC processes so that existing data put stringent constraints on the couplings.However,if only some of the operators with a particular generation structure are present in Eq.(1),then the eﬀective four-fermion Lagrangian does not violate lepton number.Similarly,the couplings can be arranged such that there are no other sources of FCNC interactions than CKM mixing in the quark sector.In the purely leptonic sector, we can restrict ourselves to the following two possibilities3:(a)one single Yukawa coupling is much larger than all the others,so that the latter can be neglected;(b)two Yukawa couplings are much larger than all the others,where both couplings violate one and the same leptonﬂavor,or both couplings violate all three leptonﬂavors.In these cases low-energy experiments are not restrictive and typically allow for couplings λ<∼0.1×(˜m/200GeV),where˜m is the mass scale of the sparticles participating in the process.The corresponding limits,derived by assuming only one non-vanishing coupling at a time,are summarized in Table1.The most stringent limits forλcan be derived from CC universality,lepton universality and the inducedνe Majorana mass[9,10].Additional constraints on products ofλandλ′couplings come from rare K and B leptonic decayprocesses[13,14].In Table 1we include those limits which are relevant for the present study.Examining all possible combinations of λand λ′couplings compatible with these bounds,it turns out that if the HERA data are interpreted as top squark production (i.e.λ′131>∼0.05),then the λ-couplings relevant for leptonic processes are very strongly constrained,λ121<0.0036,λ131<0.04,and λ123<0.048.As a result,the eﬀects on purely leptonic processes at LEP2due to slepton exchanges would be small.However,if the HERA events are due to charm squark production (i.e.λ′121>∼0.05),the rare B and K decays do not impose strong constraints on λ131or λ123and we may expect large eﬀects due to τ-sneutrino exchanges at LEP2.λ122131133232Limit0.08a0.20b0.006c0.18dCombinations constrainedK →e ±µ∓10−7B d →e ±µ∓1.8×10−4B d →e ±τ∓2.0×10−3B d →µ±τ∓2.4×10−3Table 1:Upper part:The 1σlimits on the R -parity breaking couplings λ[in units of ˜m /200GeV,where ˜m is the appropriate sfermion mass],from (a)charged-current universality;(b)Γ(τ→eν¯ν)/Γ(τ→µν¯ν);(c)the induced νe Majorana mass;(d)Γ(τ→eν¯ν)/Γ(µ→eν¯ν);(a),(b)and (d)from Ref.[10],(c)from Ref.[9].Lower part:Limits on the products of λand λ′which are relevant for our discussion [in units of (˜m /200GeV)2];K decay limits from Ref.[13],B decay limits from Ref.[14].Figure 1:Diagrams for Bhabha scattering e +e −→e +e −including s -and t -channelexchange of ˜ντ(λ131=0).We will ﬁrst consider the case (a)taking speciﬁcally λ131=0.The cross section for Bhabha scattering is then built up by the s -and t -channel exchange of γ,Z bosons and of4Figure2:Diagrams for e+e−→τ+τ−including t-channel exchange of˜νe(λ131=0). (anti-)sneutrinos˜ντ,¯˜ντ(see Fig.1).The cross section can be written most transparently in terms of helicity amplitudes[15]:dσ8 (1+cosθ)2 |f s LR|2+|f s RL|2+|f t LR|2+|f t RL|2−2Re(f s∗LR f t LR)−2Re(f s∗RL f t RL) +(1−cosθ)2 |f s LL|2+|f s RR|2 +4 |f t LL|2+|f t RR|2 (6) While the s-and t-channelγ,Z amplitudes in the Standard Model involve the coupling of vector currents,the sneutrino exchange is described by scalar currents.By performing appropriate Fierz transformations,the s-channel˜νexchange amplitudes can be rewritten, however,as t-channel vector amplitudes,and t-channel˜νexchange amplitudes as s-channel vector amplitudes:(¯e R e L)(¯e′L e′R)→−1s +g2Ls +g2Rs +g L g R2(λ1j1/e)2s +g L g R2(λ1j1/e)2 t+g2L√s =192GeV45◦≤θ≤135◦λ131=0.01λ131=0.1σtot (SM ⊕˜ντ)/σtot (SM )−1e +e −→e +e −m ˜ντ[GeV]110−110−210−310−4200300400500Figure 3:Eﬀect of sneutrino ˜ντexchange on the cross section for Bhabha scattering for 45◦≤θ≤135◦at√s =184GeV (dashed lines).6f t RL=1t−m2Z(13)f t LL=1t−m2Z+1s−m2j+iΓj m j(14)f t RR=1t−m2Z+1s−m2j+iΓj m j(15)The parameters m j andΓj are the mass and width of the sneutrino˜νj=˜ντ.To simplify notations we have deﬁned the indices L,R to denote the helicities of the ingoing electron (ﬁrst index)and the outgoing positron(second index).The helicities of the ingoing positron and the outgoing electron areﬁxed by theγ5invariance of the vector interactions:they are opposite to the helicities of the lepton partner in s-channel amplitudes and the same in t-channel amplitudes4.The left/right Z charges5of the leptons are deﬁned asg L= √πα 1/2 I l3−s2W Q lg R= √πα 1/2 −s2W Q lIn Fig.3the impact of the sneutrino˜ντexchange on the Bhabha scattering process at LEP2energies is shown as a function of the sneutrino mass,assuming couplingsλ131=0.1 orλ131=0.01.Due to the s-channel exchange,the eﬀect can be very large if the sneutrino mass is close to the LEP2center-of-mass energy.The analysis ofτ+τ−production in e+e−annihilation proceeds in an analogous way. An important diﬀerence is the absence of the t-channel Standard Model amplitude and the s-channel sneutrino exchange amplitude if only the Yukawa couplingλ131is assumed to be non-zero(i.e.λ1j1=λ131in Eqs.(10,11)and f t=0in Eqs.(12-15)).In this case theτ+τ−production process is mediated by the s-channelγ,Z exchange and the exchange of the(anti-)sneutrino˜νe in the t-channel(see Fig.2).Because the s-channel sneutrino exchange diagram is absent,the impact on the total cross section is small even forλ131as large as0.1as can be seen in Fig.4.In the scenario considered,that is forλ131=0and all other Yukawa couplings vanishing,the process e+e−→µ+µ−is not aﬀected and the cross section is given by the Standard Model.Given the bounds of Table1,electron sneutrino exchange involvingλ121cannot con-tribute toµpair production in this speciﬁcλscenario.Finally,in the realization of case(a)withλ123=0all leptonﬂavors are violated. Bhabha scattering is then not aﬀected at all.However,µ+µ−andτ+τ−pair production in e+e−scattering would receive contributions from t-channel˜ντand˜νµsneutrino exchanges, respectively(i.e.λ1j1⇒λ123in Eqs.(10,11)and f t=0in Eqs.(12-15)).Case(b)with two large Yukawa couplings is interesting if both couplings violate the same leptonﬂavor:λ131andλ232=0,for example.If this scenario is realized,then the process e+e−→µ+µ−receives an additional contribution from s-channel˜ντsneutrino exchange.Therefore,µ+µ−production would be aﬀected in a similar way as Bhabha scattering,which is apparent from Fig.4.Stringent bounds on contact interactions in the lepton sector have been reported by the LEP experiments[16,17].Deﬁning the contact interactions by the LagrangianL f,ij CI=±4π8π≃0.5to0.7TeV as an order of magnitude estimate in the present scenario.Choosing m˜ν≃200GeV,the Yukawa couplings could still be of the order0.4. This analysis is based on an integrated luminosity of L∼10pb−1at√∆A=A F B(SM⊕˜νj)−A F B(SM)∆=σtot(SM⊕˜νj)/σtot(SM)−1µ+µ−:λ131=λ232=0.1τ+τ−:λ131=0.1∆−∆∆A−∆A√s=192GeV.9m˜ν=200GeV Γ˜ν=1GeV λ131=0.145◦≤θ≤135◦σtot(e+e−→e+e−)[pb]√The cross section for the production of sneutrinos which decay to a speciﬁedﬁnal state F,is given by the Breit-Wigner formulaσ(e+e−→˜ν→F)=4πs(s−m2˜ν)2+m2˜νΓ2˜ν(17)The partial decay widthΓ(˜ν→e+e−)=λ21j1m˜ν/16πis very small.However sneutrinos canalso decay via R-parity conserving gauge couplings toνχ0and l±χ∓pairs with subsequentχ0andχ±decays and via R-parity violatingλ′couplings to q¯q pairs.The partial decay widths for these channels depend on the speciﬁc choice of the supersymmetry breakingparameters.In large regions of the supersymmetry parameter space,the total decay width of sneutrinos can be as large as1GeV,i.e.signiﬁcantly larger than the energy spread6atLEP2.In this case the interference with the background Standard Model process must betaken into account if F=e+e−orτ+τ−.The cross sections including these interference eﬀects have been presented in Eqs.(6)and(8)to(15).A representative example for thecross section of the process e+e−→e+e−including˜ντresonance formation is displayed in Fig.5.Since the width is wider than the beam energy spread,the maximum of the cross section is given by the unitarity limitσmax=(8π/m2˜ν)B2e for sneutrino and anti-sneutrinoproduction added up.The cross section in the peak region is therefore very large.In addition to theℓ+ℓ−ﬁnal states one should expect many otherﬁnal states generated in R-parity conserving˜νdecays.Examples are’Zen events’e+e−→˜ν→ν˜χ01etc.(18) with R-parity breaking˜χ01decays,or isolated lepton eventse+e−→˜ν→ℓ˜W →W˜χ01 etc.(19) in cascade decays.In addition one can also expect R-parity violating decays to quark jets ˜ν→jj[21].4SummaryIn this paper we have shown that if R-parity is broken by explicit lepton number violating operators in the leptonic sector,distinctive signals in e+e−→e+e−,µ+µ−andτ+τ−pro-cesses are predicted.Motivated by a plausible explanation of the HERA events involving the R-parity breaking LQ¯D operator,we have analysed the impact of the LL¯E operator on these leptonic processes.Interpreting the HERA data as charm squark production, the operator that violatesτ-ﬂavor is the most interesting scenario for LEP2physics.If sleptons do exist in the mass range of200GeV,the eﬀect of the sneutrino exchanges ats=192GeV at LEP2[20].LEP2could be very large.If sneutrino masses were within the reach of LEP2,sneutrinos would manifest themselves through resonance formation in e+e−collisions. AcknowledgementsNumerical cross checks have been performed with the help of CompHEP[22]adapted to the R-parity violating supersymmetry.We are grateful to G.Ross and J.S.Lee for a discussion on bounds of the couplingsλ,and to P.Wells for information on the LEP2beam energy spread.Thanks for discussions go also to P.M¨a ttig and munications by J.Holt,J.Kirkby,F.Richard,D.Treille and D.Zerwas are gratefully acknowledged. 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